/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [EQUIVALENT, 25 ms]
(6) YES


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(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

data Tup0 = Tup0 ;

compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
compareTup0 Tup0 Tup0 = EQ;

esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
esEsOrdering LT LT = MyTrue;
esEsOrdering LT EQ = MyFalse;
esEsOrdering LT GT = MyFalse;
esEsOrdering EQ LT = MyFalse;
esEsOrdering EQ EQ = MyTrue;
esEsOrdering EQ GT = MyFalse;
esEsOrdering GT LT = MyFalse;
esEsOrdering GT EQ = MyFalse;
esEsOrdering GT GT = MyTrue;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;

max0 x y MyTrue = x;

max1 x y MyTrue = y;
max1 x y MyFalse = max0 x y otherwise;

max2 x y = max1 x y (ltEsTup0 x y);

maxTup0 :: Tup0  ->  Tup0  ->  Tup0;
maxTup0 x y = max2 x y;

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

otherwise :: MyBool;
otherwise = MyTrue;

}

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(1) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

data Tup0 = Tup0 ;

compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
compareTup0 Tup0 Tup0 = EQ;

esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
esEsOrdering LT LT = MyTrue;
esEsOrdering LT EQ = MyFalse;
esEsOrdering LT GT = MyFalse;
esEsOrdering EQ LT = MyFalse;
esEsOrdering EQ EQ = MyTrue;
esEsOrdering EQ GT = MyFalse;
esEsOrdering GT LT = MyFalse;
esEsOrdering GT EQ = MyFalse;
esEsOrdering GT GT = MyTrue;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;

max0 x y MyTrue = x;

max1 x y MyTrue = y;
max1 x y MyFalse = max0 x y otherwise;

max2 x y = max1 x y (ltEsTup0 x y);

maxTup0 :: Tup0  ->  Tup0  ->  Tup0;
maxTup0 x y = max2 x y;

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

otherwise :: MyBool;
otherwise = MyTrue;

}

----------------------------------------

(3) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

----------------------------------------

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

data Ordering = LT  | EQ  | GT ;

data Tup0 = Tup0 ;

compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
compareTup0 Tup0 Tup0 = EQ;

esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
esEsOrdering LT LT = MyTrue;
esEsOrdering LT EQ = MyFalse;
esEsOrdering LT GT = MyFalse;
esEsOrdering EQ LT = MyFalse;
esEsOrdering EQ EQ = MyTrue;
esEsOrdering EQ GT = MyFalse;
esEsOrdering GT LT = MyFalse;
esEsOrdering GT EQ = MyFalse;
esEsOrdering GT GT = MyTrue;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;

max0 x y MyTrue = x;

max1 x y MyTrue = y;
max1 x y MyFalse = max0 x y otherwise;

max2 x y = max1 x y (ltEsTup0 x y);

maxTup0 :: Tup0  ->  Tup0  ->  Tup0;
maxTup0 x y = max2 x y;

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

otherwise :: MyBool;
otherwise = MyTrue;

}

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(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="maxTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="maxTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="maxTup0 vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="max2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="max1 vx3 vx4 (ltEsTup0 vx3 vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="max1 vx3 vx4 (fsEsOrdering (compareTup0 vx3 vx4) GT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="max1 vx3 vx4 (not (esEsOrdering (compareTup0 vx3 vx4) GT))",fontsize=16,color="burlywood",shape="box"];15[label="vx3/Tup0",fontsize=10,color="white",style="solid",shape="box"];8 -> 15[label="",style="solid", color="burlywood", weight=9];
15 -> 9[label="",style="solid", color="burlywood", weight=3];
9[label="max1 Tup0 vx4 (not (esEsOrdering (compareTup0 Tup0 vx4) GT))",fontsize=16,color="burlywood",shape="box"];16[label="vx4/Tup0",fontsize=10,color="white",style="solid",shape="box"];9 -> 16[label="",style="solid", color="burlywood", weight=9];
16 -> 10[label="",style="solid", color="burlywood", weight=3];
10[label="max1 Tup0 Tup0 (not (esEsOrdering (compareTup0 Tup0 Tup0) GT))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="max1 Tup0 Tup0 (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="max1 Tup0 Tup0 (not MyFalse)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="max1 Tup0 Tup0 MyTrue",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="Tup0",fontsize=16,color="green",shape="box"];}

----------------------------------------

(6)
YES